How do you evaluate cot [sin^-1 (- sqrt2 / 3)]?

May 20, 2016

$\pm \sqrt{\frac{7}{2}}$

Explanation:

Let $a = {\sin}^{- 1} - \frac{\sqrt{2}}{3}$. Then,$\sin a = - \frac{\sqrt{2}}{3} < 0$.

Accordingly, a is in the 3rd quadrant or in the 4th.

So, $\cos a = \pm \sqrt{1 - {\sin}^{2} a} = \pm \frac{\sqrt{7}}{3}$.
The answer is $\cot a = \cos \frac{a}{\sin} a = \pm \sqrt{\frac{7}{2}}$.